\section{Tests and Examples}\label{sec:Tests}

For the assessment of FOODIE capabilities three different tests are discussed:

\begin{itemize}
  \item Oscillation equations IVP: this test is a pure ODEs, non-stiff problem;
  \item Lorenz equations IVP: this test is a pure ODEs, stiff problem;
  \item 1D Euler equations IVP: this test is a PDEs problem;
  \end{itemize}

With the first two pure ODEs tests we assess the accuracy of the FOODIE built-in solvers and demonstrate how to use the library in real applications. The last test discussion is mainly devoted to the demonstration of FOODIE application into a real, complex PDEs problem.

\input{src/tests/oscillation/oscillation.tex}
